Quasielastic neutron scattering (QNS) was used to measure the mobility of water in tuff at low saturation. The tuff sample is from a surface outcrop of the Calico Hills formation, which lies below the proposed location for a high-level nuclear waste repository, at Yucca Mountain, NV. The sample is a devitrified tuff composed mainly of zeolites and having clinoptilolite (approximately 70%), mordenite, and opal-CT as major constituents. The sample is an air dry, intact core sample. QNS measurements were made in the range 200 K to 423 K. Rotational motion of adsorbed water is easily observable and translational motion is observable at higher temperatures. The tuff data are analyzed to determine the rotational diffusion coefficient and the translational diffusion coefficient. The results yield a translational diffusion coefficient in the tuff that is significantly lower than that of bulk water but higher than for water in montmorillonite or vermiculite clays.